基于均衡通量重构的目标导向误差估计，用于涡流问题中谐波近似公式的计算

IF 2.3 2区数学 Q1 MATHEMATICS, APPLIED

IMA Journal of Numerical Analysis Pub Date : 2024-01-29 DOI:10.1093/imanum/drad107

Emmanuel Creusé, Serge Nicaise, Zuqi Tang

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引用次数: 0

摘要

在这项工作中，我们针对涡流问题建模过程中出现的谐波 $\textbf {A}$-$\varphi $ 公式提出了一种面向目标的后验误差估计方法，该方法由不符合有限元方法近似得出。它以解决与初始问题相关的邻接问题为基础。对于这两个问题中的每一个问题，都会利用一些通量重构来开发一个有保证的平衡估计器。通过这些通量，还可以获得一个目标导向误差估计器，该估计器完全可计算，并可分为主部和余部。数值实验对我们的理论结果进行了说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Goal-oriented error estimation based on equilibrated flux reconstruction for the approximation of the harmonic formulations in eddy current problems

In this work, we propose an a posteriori goal-oriented error estimator for the harmonic $\textbf {A}$-$\varphi $ formulation arising in the modeling of eddy current problems, approximated by nonconforming finite element methods. It is based on the resolution of an adjoint problem associated with the initial one. For each of these two problems, a guaranteed equilibrated estimator is developed using some flux reconstructions. These fluxes also allow to obtain a goal-oriented error estimator that is fully computable and can be split in a principal part and a remainder one. Our theoretical results are illustrated by numerical experiments.

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来源期刊

IMA Journal of Numerical Analysis 数学-应用数学

CiteScore

5.30

自引率

4.80%

发文量

审稿时长

6-12 weeks

期刊介绍： The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.